m-Polar fuzzy ideals of BCK/BCI-algebras

Al-Masarwah, Anas; Ahmad, Abd Ghafur

doi:10.1016/j.jksus.2018.10.002

Cited by 56 publications

(50 citation statements)

References 13 publications

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“…An mp-fuzzy setˆ on a BCK/BCI-algebra X is called an m-polar fuzzy ideal (briefly, mp-fuzzy ideal) of X (see [32] Definition 3.7) if the following conditions are valid.…”

Section: Preliminariesmentioning

confidence: 99%

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Multipolar Fuzzy p-Ideals of BCI-Algebras

et al. 2019

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The notion of (normal) m-polar ( ∈ , ∈ ) -fuzzy p-ideals of BCI-algebras is introduced, and several properties are investigated. Relations between an m-polar ( ∈ , ∈ ) -fuzzy ideal and an m-polar ( ∈ , ∈ ) -fuzzy p-ideal are displayed, and conditions for an m-polar ( ∈ , ∈ ) -fuzzy ideal to be an m-polar ( ∈ , ∈ ) -fuzzy p-ideal are provided. Characterization of m-polar ( ∈ , ∈ ) -fuzzy p-ideals are considered. Given an m-polar ( ∈ , ∈ ) -fuzzy ideal (resp., m-polar ( ∈ , ∈ ) -fuzzy p-ideal), a normal m-polar ( ∈ , ∈ ) -fuzzy ideal (resp., normal m-polar ( ∈ , ∈ ) -fuzzy p-ideal) is established. Using an m-polar ( ∈ , ∈ ) -fuzzy ideal, the quotient structure of BCI-algebras is constructed.

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“…An mp-fuzzy setˆ on a BCK/BCI-algebra X is called an m-polar fuzzy ideal (briefly, mp-fuzzy ideal) of X (see [32] Definition 3.7) if the following conditions are valid.…”

Section: Preliminariesmentioning

confidence: 99%

“…In 2014, Chen et al [26] introduced an m-polar fuzzy set, which is an extension of bipolar fuzzy sets. m-polar fuzzy sets have been applied to decision-making problems (see [27]), graph theory (see [28][29][30][31]), and BCK/BCI-algebra (see [32]).…”

Section: Introductionmentioning

confidence: 99%

Multipolar Fuzzy p-Ideals of BCI-Algebras

et al. 2019

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“…Applying the idea of m-pF sets to group theory, Farooq et al [30] initiated the concept of m-pF subgroups, and investigated some of their properties. Furthermore, Al-Masarwah and Ahmad [31] applied m-pF sets to BCK/BCI-algebras. They presented the concepts of m-pF subalgebras, m-pF ideals, and m-pF commutative ideals, and investigated related results.…”

Section: Introductionmentioning

confidence: 99%

m-Polar ( α , β ) -Fuzzy Ideals in BCK/BCI-Algebras

Al-Masarwah

Ahmad

2019

Symmetry

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Multi-polar vagueness in data plays a prominent role in several areas of the sciences. In recent years, the thought of m-polar fuzzy sets has captured the attention of numerous analysts, and research in this area has escalated in the past four years. Hybrid models of fuzzy sets have already been applied to many algebraic structures, such as B C K / B C I -algebras, lie algebras, groups, and symmetric groups. A symmetry of the algebraic structure, mathematically an automorphism, is a mapping of the algebraic structure onto itself that preserves the structure. This paper focuses on combining the concepts of m-polar fuzzy sets and m-polar fuzzy points to introduce a new notion called m-polar ( α , β ) -fuzzy ideals in B C K / B C I -algebras. The defined notion is a generalization of fuzzy ideals, bipolar fuzzy ideals, ( α , β ) -fuzzy ideals, and bipolar ( α , β ) -fuzzy ideals in B C K / B C I -algebras. We describe the characterization of m-polar ( ∈ , ∈ ∨ q ) -fuzzy ideals in B C K / B C I -algebras by level cut subsets. Moreover, we define m-polar ( ∈ , ∈ ∨ q ) -fuzzy commutative ideals and explore some pertinent properties.

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“…In 2014, Chen et al [6] introduced an m-polar fuzzy set which is an extension of bipolar fuzzy set. The m-polar fuzzy set applied to decision making problem (see [1]) and BCK/BCI-algebra (see [2,3,15]). The notion of m-polar fuzzy set is applied to hyper BCK-algebra.…”

mentioning

confidence: 99%

“…• a strong hyper BCK-ideal of H (see [12]) if it satisfies (2) and (∀x, y ∈ H)((x • y) ∩ A = ∅, y ∈ A ⇒ x ∈ A).…”

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confidence: 99%

Multipolar fuzzy hyper BCK-ideals of hyper BCK-algebras

Jun

2020

JAHLA

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In this paper, we apply m-polar fuzzy set to hyper BCKalgebra. We introduce the notions of k-polar fuzzy hyper BCK-ideal, k-polar fuzzy weak hyper BCK-ideal, k-polar fuzzy s-weak hyper BCK-ideal, k-polar fuzzy strong hyper BCK-ideal and k-polar fuzzy reflexive hyper BCKideal, and investigate related properties and their relations. We discuss k-polar fuzzy (weak, s-weak, strong, reflexive) hyper BCK-ideal in relation to k-polar level set. Article InformationThe hyper algebraic structure was introduced by F. Marty [14] in 1934. Bolurian et al. [5] was introduced hyper BCK-algebra as an extension of BCK-algebra. Since then, many scholars have been studying hyper BCK-algebra and its infrastructure and so on. In addition, research using fuzzy and soft set is actively being carried out (see [4], [7], [8], [9], [11]). In 2014, Chen et al. [6] introduced an m-polar fuzzy set which is an extension of bipolar fuzzy set. The m-polar fuzzy set applied to decision making problem (see [1]) and BCK/BCI-algebra (see [2,3,15]).The notion of m-polar fuzzy set is applied to hyper BCK-algebra. The concepts of k-polar fuzzy (weak, s-weak, strong, reflexive) hyper BCK-ideal are introduced, and the relations and properties are investigated in relation to k-polar level set. PreliminariesLet H be a nonempty set endowed with a hyperoperation "•". For two subsets A and B of H, denote by A • B the set a∈A,b∈B a • b. We shall use x • y instead of x • {y}, {x} • y, or {x} • {y}.By a hyper BCK-algebra (see [13]) we mean a nonempty set H endowed with a hyperoperation "•" and a constant 0 satisfying the following axioms:

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m-Polar fuzzy ideals of BCK/BCI-algebras

Cited by 56 publications

References 13 publications

Multipolar Fuzzy p-Ideals of BCI-Algebras

Multipolar Fuzzy p-Ideals of BCI-Algebras

m-Polar ( α , β ) -Fuzzy Ideals in BCK/BCI-Algebras

Multipolar fuzzy hyper BCK-ideals of hyper BCK-algebras

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